: u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs

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1 15 C11-4 Numerical analysis of flame propagation in a combustor of an aircraft gas turbine, ( ) 1-1 imamura ( ) 1-1 tsuru Takuji TOMINAGA, School of Mechanical Engineering, the University of Tokyo, Komaba, Meguro-ku, Tokyo Nobuyuki TANIGUCHI, Information Technology Center, the University of Tokyo, Yayoi, Bunkyo-ku, Tokyo Yuichi ITOH, Institute of Industrial Science, the University of Tokyo, Komaba, Meguro-ku, Tokyo Toshio KOBAYASHI, Institute of Industrial Science, University of Tokyo, Komaba, Meguro-ku, Tokyo Akira IMAMURA, Kawasaki Heavy Industries, LTD., 1-1 Kawasaki-cho, Akashi-city, Hyogo Tomoko TSURU, Kawasaki Heavy Industries, LTD., 1-1 Kawasaki-cho, Akashi-city, Hyogo A large eddy simulation (LES) and a G-equation based on flamelet concept are demonstrated in engineering design for a premixed aircraft gas-turbine combustor. G-equation model is extended for combustion in a non-uniform equivalent ratio of premixed gas. The simulations of the flame propagation are executed in some conditions with different relations of the equivalent ratios, and as a result, the flame positions and propagating behaviors depend on the equivalent ratios Fig.1 16 NOx Large Eddy Simulation (LES) G LES 1 G flamelet [1][2] G Fig.1: The combustor and the one sector model Copyright c 21 by JSCFD

2 : u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs S ij : (= P ρ ) : Schmidt : SGS : Schmidt LES s L : S : = {( i,j (S2 ij )} 1 2 G ξ s L s T δ φ main φ pilot r R : s L (ξ, T,...) s L (ξ) (6) : : : s L (ξ) : : : : : ξ t + u jξ = {( ν + ν ) } SGS ξ (7) x j x j S c S csgs x j 4. G flamelet : i (i = 1, 2, 3) G G G < G : a G > G G 1 : i G =.5 LES : G G : t + u jg = s L G (u j G u j G) (5) x j x j : : G s : L : s : LES L Müller et al. [4] RANS (5) G LES 1 s T u i t + u iu j = p + ( ν u ) i τ ij (1) x j x i x j x j s L G = s T G (8)

3 { } s T (u /s L ) 2 = exp s L (s T /s L ) 2 (9) u = S (1) s T (9) Yakhot et al. [7] u s T (s T /s L ) 2 s L u (1) (5) 2 (u j G u j G) = ν SGS σ G G x j (11) 5.2 σ G SGS σ G σ G =.25 PIV [6] ( ) δ free-slip g (12) s L g = S (13) g (13) LES δ Göttgens et al. [8] Tab.2 5. Tab.1 Tab.1: Computational condition Reynolds Number 596 Pressure P(MPa).113 Temperature T(K) 623 Fuel Methane-Air Equivalent ratio φ main.4, φ pilot.7 Fig.2 22 ( ) ( ) 59 Fig.2: Computational grid Tab.2: Computational method Method for flow field (LES Kogaki(1999)) Coupling algorithm fractional step method ( t = [sec]) SGS model Smagorinsky model (C S =.1) Spatial differential scheme Second-order central differential scheme Time advancing scheme (advection term) Second-order Adams-Bashforth scheme (diffusion term) Crank-Nicolson scheme Stabirizing method 6th-order explicit filter Method for flame propagation (Scalar G) Spatial differential scheme (advection term) QUICK (diffusion term) Second-order central differential scheme Time advancing scheme Second-order Adams-Bashforth scheme G ξ 37step HITACHI SR8(

4 1 node(8cpu) Fig LES <u> LES on(2) on(2) 6 Exp.on(2) <u> Exp.on(2) Fig.4: The axial velocity at the center of a sector Fig.5: The tangential velocity at the center of a sector Fig.3 37step Fig.4 Fig.5 Fig.4 ( =.65.7) Fig.4 ( =.75 1) Fig.5 ( =.6.7) Fig <u> LES on(1) <u> Exp.on(1) 5 <w> LES LES on(1) on(1) 4 <w> Exp.on(1) Exp.on(1) <w> LES on(2) LES on(1) on(2) 4 Exp.on(2) <w> Exp.on(1) Exp.on(2) Fig.3: Contours of the instantaneous axial velocity

5 =.95 free-slip Mach NEDO 6.2 Tab.1 2 [1] Menon, S., Large-eddy simulation of combustion instabilities, Proceedings of the Sixth International Confer- 2 1 ence on Numerical Combustion, φ pilot =.7 φ main =.4 [2],,, , B(21), pp φ pilot =.7 φ main =.6 [3],,, 21 Fig.7 [4] Müller, C. M., Breitbach, H., and Peters, N., Twenty- G Fifth Symposium (International) on Combustion / The 12ms 6ms G Combustion Institute, pp , 1994 [5],, φ pilot =.7, p. 15, [6] 63-69, B(1997), pp φ main =.4 G [7] Yakhot, V., Propagation Velocity of Premixed Turbulent Flames,Combustion Science and Technology, Vol.6,1988 φ main =.6 [8] Göttgens, J., Mauss, F. and Peters, N., Twenty-Fourth G >.5 Symposium (International) on Combustion / The Combustion Institute, pp , [9],,, , B(1999), pp LES G 8.

6 Fig.6: Time evolution of flame (Contour of scalar G) (φ main =.4 φ pilot =.7) Fig.7: Time evolution of flame (Contour of scalar G) (φ main =.6 φ pilot =.7)

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